# Calculate the Odds

I subscribe to the mastery method of education when it comes to The Three “R’s”. If you don’t know a concept, I see no point in “pushing on”. Once you understand the theory, however, is it okay to cut some corners?

Arithmetic is probably the most obvious area where this applies. We teach a new lesson and have our children do multiple practice work, showing they have command of the concept. We watch them proceed with fluency and then perhaps reduce their work slightly as they progress.

Calculator or no calculator; that is the question.

Once mastery is achieved, is it okay to let them use helps; mainly, a calculator? Am I going to somehow damage the work already done and undo necessary wrinkles if I let them cheat and use a device to help them reach their answers faster? Is using a calculator even cheating?

Honestly, I don’t have an answer for you. (Sad; isn’t it?) However, I do have some thoughts and perhaps some ideas.

I think letting our children use “helps” on a regular basis will retard their learning. Meaning: they will slowly begin to lose the knowledge of how to work without the aid of helps. So, using them all the time would be harmful. I also think never letting them use helps might be a concern, especially when it comes to higher maths. (Sheesh; one problem could take hours.) Therefore, I suggest balance.

Therein lies the tricky part. When do we allow the use of helps and when should we not? Again, I have no straightforward answers. (I really am troublesome today, aren’t I?) Each family must decide for themselves the correct method.

I do not believe helps are a good idea for the littlest youngsters; again, they need to first master the concepts. So, helps are not an option for them. Sorry, guys!

For the middle-aged kiddos, it gets a little trickier. Here is where the balance comes in. For our family, daily work must be done by hand. I want to see the work and the path which got them to the end result. (Method is just as important as finding the right answer.) During test times and the occasional quiz, this is where a calculator might be made available. I find that allowing them the use of helps keeps them moving quickly and keeps them from being frustrated with a four page test.

High school kids are pretty much free to choose, as far as I am concerned. At this point in their learning, they are doing advanced math with graphing calculators and extensive theorems; I would hate for them not to use helps, the poor things. I would still give an occasional pop quiz, to make sure the fundamentals are good to go, but, overall, helps are acceptable.

Honestly, I don’t think this idea would have ever popped up for us if it hadn’t been for SAT testing (standardized testing, not college) with our PSP last year. I fully intended for “T” to use a scratch paper and pencil during the arithmetic section of her test. The school suggested a calculator though, for the exact reasons listed above. This opened up whole new avenues of thought for me and I’m glad we had the opportunity to reflect. “T” was more relaxed and able to focus knowing her only concern was method and not spending so much time doing the calculations.

Thus far, our plan is working. The kids are progressing nicely in their learning and we are appreciating the compromise. Now; if I could only get over the nagging feeling that this is somehow cheating….

How about your family? Do you allow “helps” during your learning day?

## 13 thoughts on “Calculate the Odds”

1. Such a thought provoking article. I agree with you, it’s a tricky one! I think there are some things that “helps” like a calculator are brilliant for and with more complex mathematical questions, even necessary, but I think that it is important first to have a solid grounding in the basics. If not, you can end up with a wildly incorrect answer due to mispressing keys on a calculator and not able to notice, let alone be able to correct it. I think it’s so important that we know how to use things like calculators, spreadhsheets etc to help us – these are skills so needed in later life. My problem is with the younger ones – it’s the method, especially the mental methods and being confident with numbers and how they work. With my 3 year old, we’re just starting to look at adding. He loves doing this by counting objects and his fingers. In a while, when he’s confident – I might give him some “wrong” calculations that I’ve performed on a calculator and get him to work them out himself and then check how I’ve gone wrong. I’m hoping it will help him to work out that whilst “helps” are useful, they are not infallible! I think you’re right – there are no hard and fast rules, it’s just a what works for your child kind of thing. There will probably be some children for a whom a calculator will be a super fun way of not having to do any work themselves whereas others will be so keen to work everything out, they won’t like the calculator doing the work for them – and then everyone in between! Thanks for sharing this – it’s really made me think!

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2. I don’t think so. Not yet anyway. But I only have a 4th and 2nd grader. However, I do encourage them to use “clues” around them, and I don’t call that cheating. I call that “awareness development.” So if a spelling word, phonics rule, multiplication fact, map, or globe just so happens to be in the room we are in doing our work that day, I won’t remove the “helps”–but neither do I point them out. If they think to use them when prompted with related material, I’m grateful they are thinking and scanning their environment! Calculators I’ll probably bring in around Math 6/7 for Saxon Math, but I’ll try to hold off as long as possible. For advanced Saxon math, they will be required to do graphing by hand for quite awhile until they prove to me they understand. I don’t think I was allowed a graphing calculator in high school until calculus. (Loved my math teacher.) Of course, everything may change when I actually get there in the trenches, right! LOL! Good post to think about! Thanks!

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3. I have a 6th grader and he is now being asked to use calculator with some of his math lessons. I have let him use one a little in the past to check answers. So when he was asked to use it now it he has a real understanding of how the calculator works. Sounds funny with all the tech that’s out there but a simple calculator can be pretty frustrating to use. Great post!

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4. Since my older children al went to public school and were required to have a calculator in Algebra and used if from that point on… I have done the same with my youngest I am homeschooling. I do like that you said mastery is the key to moving on. That is exactly why I chose to homeschool. He had not mastered phonetics and they had no intention of doing remedial work necessesary. I am so glad to have found the program geared to 3rd graders up to adults that matched his intelligence level and didn’t dumb it down. Can you believe the school repeatedly told me that with his intelligence he would get past this…. Learning coping skills of guessing synonyms based on the content for words he couldn’t read was ok by them… sorry getting off my soap box now…

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5. I’m a paper, pencil (and eraser!) kind of teacher. Primarily because I struggled with math and don’t want my student to struggle in the same way. For our homeschool, it’s important to really have the concept and the mechanics down, accurately, before regular use of the calculator. That said, I do not consider using a calculator cheating – more a short-cut or a tool. Likely because I use a calculator, and other tools regularly for expediency and don’t consider myself to be cheating!

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6. We struggle with this too! My oldest (in 5th grade) would love for me to let him use a calculator, but I just can’t do it yet. Even though he does pretty well with long division and multiplication in the thousands, I feel like I want him to keep working it out on paper until he can fly through it as quickly as an adult. I don’t want him to get “rusty” as he moves onto higher math concepts.

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7. Wow; this sure has caused a lot of good conversation. I appreciate all the feedback! 🙂

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8. In the A Beka curriculum, scientific calculators were required for the higher maths and science because the sine, cosines and pi strategies were so time consuming. But – they specified exactly which problems the calculators were to be used on. No calculators until the third year of high school.

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• Thanks for the heads up! 🙂

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9. I’ve successfully circumvented the problem of deciding whether or not to use a calculator. My solution is to not do any math. Problem solved. There, I said it.

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• Well; I’m glad we solved that problem. 🙂

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10. I do agree with you. Honestly, my little blessings are to young for calculators, but I have thought about this before, and I also believe that moderation and balance would be the option for us as well.

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11. I agree. Calculators are so easy to learn how to use. Might as well put that off until the testing requires it. It’s much more important, during the elementary and middle years, to master calculating and memorizing math, for sure.

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